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ACM Symposium on Theory of Computing (STOC)

Multiparty unconditionally secure protocols

David Chaum, Claude Crépeau, Ivan Damgård

Published Jan 1, 1988• 1,556 citations
Publisher

Abstract

Under the assumption that each pair of participants em communieatc secretly, we show that any reasonable multiparty protwol can be achieved if at least Q of the Participants am honest. The secrecy achieved is unconditional, It does not rely on any assumption about computational intractability. 1.
DOI
10.1145/62212.62214

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Under the assumption that each participant can broadcast a message to all other participants and that each pair of participants can communicate secretly, we present a verifiable secret sharing protocol, and show that any multiparty protocol, or game with incomplete information, can be achieved if a majority of the players are honest. The secrecy achieved is unconditional and does not rely on any assumption about computational intractability. Applications of these results to Byzantine Agreement are also presented.
Multiparty computation considers the design of protocols such that a set of n users U] ... lim each with their own secret input Xi, can compute a function Y =F(x], ... , x/J. In this paper, we study a requirement for devising non-interactive multiparty computation protocols and present the first non-interactive multiparty computation protocol, which has the following advantages: a) The amount of computation required by each participant is equal to the amount of computation in an ideal model (i.e. the proposed scheme is optimal). b) In the presence of passive adversaries, no set of less than n users can leam more than what is allowed in the underlying secret sharing scheme (other than the function value), c) In the presence of active adversaries (i.e, Byzantine faults are allowed), no set of less than nl2 users can either leam more than what is allowed in the underlying secret sharing scheme, nor can they dismpt the computation. d) The partial security provided in our scheme is unconditional. That is, the proposed scheme does not rely on any non-proven cryptographic assumption.
Two settings are traditionally considered for secure multiparty computation, depending on whether or not a majority of the parties are assumed to be honest. Existing protocols that assume an honest majority provide “full security” (and, in particular, guarantee output delivery and fairness) when this assumption holds, but are completely insecure if this assumption is violated. On the other hand, known protocols tolerating an arbitrary number of corruptions do not guarantee fairness or output delivery even if only a single party is dishonest. It is natural to wonder whether it is possible to achieve the “best of both worlds”: namely, a single protocol that simultaneously achieves the best possible security in both the above settings. Here, we rule out this possibility (at least for general functionalities) and show some positive results regarding what can be achieved.
Two settings are traditionally considered for secure multiparty computation, depending on whether or not a majority of the parties are assumed to be honest. Protocols designed under this assumption provide “full security ” (and, in particular, guarantee output delivery and fairness) when this assumption holds; unfortunately, these protocols are completely insecure if this assumption is violated. On the other hand, protocols tolerating an arbitrary number of corruptions do not guarantee fairness or output delivery even if only a single party is dishonest. It is natural to wonder whether it is possible to achieve the “best of both worlds”: namely, a single protocol that simultaneously achieves the best possible security in both the above settings. Here, we rule out this possibility (at least for general functionalities) but show some positive results regarding what can be achieved.